A quick question on the twin paradox (quick I promise!)

nrqed

I am reading ''Modern Physics`by Tipler and Llewellyn, 4th edition, page 52.

They say something which, unless I am completely confused, is completely wrong.

I cite (Ulysses is the twin in the spaceship, they use [itex] \Delta t_{Earth}= \gamma \Delta_{spaceship}[/itex] and then say:

''...we cannot do the same analysis in the frame of the spaceship because it does not remain in an inertial frame during the round trip; hence it falls outside of the special theory and no paradox arises,. The laws of physics can be formulated so as to be invariant for accelerated observers, which is the role of general relativity''

(emphasis mine).

As far as I understand, this entire paragraph is completely wrong. There is no problem treating accelerated observers in SR. I am surprised to see this in a fairly recent textbook (2003).

Am I totally in the left field?

George Jones

You're right - special relativity can be used to compare the wristwatches of accelerated twins in Minkowski spacetime.

The book Spacetime Physics by Taylor amd Wheeler, first published in the 60's, does this in a worked exercise.

This is a myth that refuses to die.

Regards,
George

nrqed

Thanks,

Indeed...But it is no tsuprising that it is still such a strong myth when a *textbook* perpetuates this explicitly. I was flabbergasted to see this in a textbook!!

robphy

Part of the problem is that, for many, "SR" is only about "inertial frames" and non-inertial frames are only treated in "GR".

Of course, the modern view distinction is that "SR" deals with zero-curvature-R⁴ spacetimes, "GR" handles generally-curved spacetimes on general manifolds (of which SR is a special case).

In this light, the above is like saying that "Euclidean geometry" is only about Cartesian coordinates and
polar coordinates are only treated in "Riemannian geometry".

Here's one of my favorite papers on the clock paradox:
http://links.jstor.org/sici?sici=000...3E2.0.CO%3B2-L
"The Clock Paradox in Relativity Theory"
Alfred Schild
The American Mathematical Monthly, Vol. 66, No. 1. (Jan., 1959), pp.1-18.

George Jones

And I think that there are other books that say the same thing, unfortunately.

I think that part of the problem is that often relativity (both SR and GR) does not really receive enough attention in the undergraduate and graduate curricula, so that people that write general texts sometimes didn't see much relativity when they were students.

I understand the reasoning - there are so many subjects to cover that some topics necessarily receive superficial treatment - but this is a shame, because there are now so many nice relativity books from which to choose.

Regards,
George

neutrino

Apart from Wheeler and Taylor, are there any other SR books that discuss the topic of non-inertial frames in SR?

George Jones

A Traveler's Guide to Spacetime by Moore, a very nice introduction to special relativity, mentions acceleration, but doesn't go into a lot of detail. The Geometry of Minkowski Spacetime by Naber treats acceleration, but this book is maybe meant more for math students than physics students.

As pervect has mentioned a number of times, a nice advanced treatment of acceleration in SR is chapter 6 of Gravitation by Misner, Thorne, and Wheeler.

Regards,
George

neutrino

Thanks. I would prefer a proper textbook treatment, and hopefully, one fine day I'll get that BIG, black textbook. Thanks also to nrqed for this thread. Prior to this I wasn't aware of the treatment of NI frames in SR.